Problem 3 - Elementary Algebra

Question

For the following problems, convert each fraction to a percent. $$ \frac{1}{8} $$

Step-by-Step Solution

Answer

Answer: The fraction $$\frac{1}{8}$$ is equal to $$12.5\%$$ when expressed as a percentage.

Step 1: Divide the numerator by the denominator

Divide the numerator (1) by the denominator (8) to get the decimal equivalent of the fraction. $$ \frac{1}{8} = 0.125 $$

Step 2: Convert decimal to percent

To convert the decimal to a percent, multiply by 100 and add the percent symbol (%). $$ 0.125 \times 100 = 12.5\% $$ The fraction $$\frac{1}{8}$$ is equal to $$12.5\%$$ when expressed as a percentage.

Key Concepts

Fractions

Fractions are a way of representing parts of a whole. A fraction consists of a numerator, the top number, and a denominator, the bottom number. The numerator tells us how many parts we have, whereas the denominator tells us into how many parts the whole is divided.
For example, in the fraction \( \frac{1}{8} \), the numerator is 1, and the denominator is 8. This means that we have one part out of eight equal parts.
Understanding fractions is crucial because they are used commonly in various fields, such as cooking, finance, and science, to represent parts of a whole. Simplifying fractions or converting them into other forms like decimals or percentages can make them easier to work with in different situations.

Percentages

Percentages are another way of expressing numbers, similar to fractions and decimals, but they specifically represent proportions out of 100. The term "percent" means per hundred. So, when you see a percentage, it's telling you how many parts out of 100 something is.
For instance, 50% means 50 parts out of 100, which is also equivalent to \( \frac{1}{2} \) or 0.5 as a decimal. When converting a fraction to a percentage, such as \( \frac{1}{8} \), first convert it to a decimal (0.125) and then multiply by 100 to get the percentage (12.5%).
Being comfortable with percentages is very useful in real-life situations, such as calculating discounts during shopping, understanding statistics, or even determining interest rates in financial contexts.

Decimal Conversion

Converting fractions to decimals is a fundamental skill in math. To convert a fraction to a decimal, you simply divide the numerator by the denominator. This process can often be done quickly with a calculator, or sometimes even mentally for simple fractions.
For example, to convert \( \frac{1}{8} \) to a decimal, you divide 1 by 8. This will give you a decimal result of 0.125. Decimal numbers make it easier to perform arithmetic operations like addition, subtraction, multiplication, and division.
Once you have a fraction in decimal form, it becomes straightforward to convert that decimal to a percentage by multiplying by 100. Understanding decimal conversion helps in simplifying complex numbers and is widely applicable in various STEM fields, making calculations more intuitive and less error-prone.